Question

在△ABC中2asinA=(2b+c)sinB+(2c+b)sinC （1）求A

Answer 1

1.2asinA=(2b+c)sinB+(2c+b)sinC 正弦定理

2a^2=2b^2+bc+2c^2+bc

a^2=b^2+c^2+bc

cosA=(b^2+c^2-a^2)/2bc=-1/2 A=120°

2.A=120° B=60°-C

sinB+sinC=sin(6°-C)+sinC

=√3/2cosC-1/2sinC+sinC

=√3/2cosC+1/2sinC

=sin(C+60°)=1

C=30°

B=30°

△ABC的为等腰三角形